Pseudo asymptotically periodic integral solution of partial neutral functional differential equations

Abstract

In this paper, we propose a new class of functions called $\mu$-pseudo $\mathcal{S}$-asymptotically periodic function on $\mathbb{R}$ by the measure theory. Furthermore, the existence, uniqueness of $\mu$-pseudo $\mathcal{S}$-asymptotically periodic integral solution to partial neutral functional differential equations with finite delay are investigated. Here we assume that the undelayed part is not necessarily densely defined and satisfies the Hille-Yosida condition.